Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity

Accounting for the complexity of psychological theories requires methods that can predict not only changes in the means of latent variables - such as personality factors, creativity, or intelligence - but also changes in their variances. Structural equation modeling (SEM) is the framework of choice for analyzing complex relationships among latent variables, but the modeling of latent variances as a function of other latent variables is a task that current methods only support to a limited extent. In this article, we develop a Bayesian framework for Gaussian distributional SEM, which broadens the scope of feasible models for latent heteroscedasticity. We use statistical simulation to validate our framework across four distinct model structures, in which we demonstrate that reliable statistical inferences can be achieved and that computation can be performed with sufficient efficiency for practical everyday use. We illustrate our framework's applicability in a real-world case study that addresses a substantive hypothesis from personality psychology.